题目大意
给一个数$n$，要判断$n$是否为素数？
题目分析
复习一下Miller-Rabin。
模板题，学习笔记见这里。
代码
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using namespace std;
typedef long long LL;
inline const LL Get_Int() {
LL num=0,bj=1;
char x=getchar();
while(x<'0'||x>'9') {
if(x=='-')bj=-1;
x=getchar();
}
while(x>='0'&&x<='9') {
num=num*10+x-'0';
x=getchar();
}
return num*bj;
}
LL Quick_Pow(LL a,LL b,LL p) {
LL sum=1;
for(; b; b>>=1,a=a*a%p)if(b&1)sum=sum*a%p;
return sum;
}
const int TIMES=20;
mt19937 g(rand());
bool Miller_Rabin(LL n) {
srand(time(NULL));
for(int i=1; i<=TIMES; i++) {
LL a=g()%(n-1)+1;
if(Quick_Pow(a,n-1,n)!=1)return false;
}
return true;
}
LL n;
int main() {
while(~scanf("%lld",&n))puts(Miller_Rabin(n)?"Yes":"No");
return 0;
}
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using namespace std;
typedef long long LL;
inline const LL Get_Int() {
LL num=0,bj=1;
char x=getchar();
while(x<'0'||x>'9') {
if(x=='-')bj=-1;
x=getchar();
}
while(x>='0'&&x<='9') {
num=num*10+x-'0';
x=getchar();
}
return num*bj;
}
LL Quick_Pow(LL a,LL b,LL p) {
LL sum=1;
for(; b; b>>=1,a=a*a%p)if(b&1)sum=sum*a%p;
return sum;
}
const int TIMES=10;
mt19937 g(rand());
bool Witness(LL a,LL n) {
LL u=n-1,t=0;
while(u%2==0)t++,u>>=1;
LL x=Quick_Pow(a,u,n);
if(x==1)return false;
for(int i=1; i<=t; i++,x=x*x%n)
if(x!=n-1&&x!=1&&x*x%n==1)return true;
return x!=1;
}
bool Miller_Rabin(LL n) {
if(n==2)return true;
if(n<2||!(n&1))return false;
srand(time(NULL));
for(int i=1; i<=TIMES; i++) {
LL a=g()%(n-1)+1;
if(Witness(g()%(n-1)+1,n))return false;
}
return true;
}
LL n;
int main() {
while(~scanf("%lld",&n))puts(Miller_Rabin(n)?"Yes":"No");
return 0;
}
